This invention relates to a method for producing a subsurface electrical resistivity model. More specifically, this invention relates to a method for resistivity modeling for locating anomalies, such as groundwater, leaks, tree roots, and other vegetation, beneath and around existing structures. A regression correlation is performed on the raw resistivity data to create a resistivity model, which is converted to graphical form, then analyzed to detect and locate subsurface soil anomalies. In an alternative embodiment, the resistivity model is compared to resistivity data from soil samples taken from around the building to determine the existence and extent of subsurface anomalies.
Detecting and locating fluid leaks beneath slab-on-grade foundations is often a difficult and destructive task. Because the slab blocks access to the soil underneath, one must either break up the slab to inspect the subjacent soil or drill relatively large holes through the slab to bore soil samples. Further, these methods require a certain amount of guesswork because of the uncertain location of suspected leaks. Consequently, a number of holes must be drilled or even jack hammered through the slab before the actual leak is located.
A less destructive method of detecting and locating leaks beneath slab foundations involves directing a radar signal down through the slab and into the subjacent soil. Because the radar return from wet soil will differ from that of dry soil, using radar may allow one to approximate a leak location without partially destroying the slab. However, certain types of reinforced slab foundations may attenuate the radar signal sufficiently such that an accurate return from the subjacent soil is unobtainable. Moreover, radar is not well suited to detecting small leaks, nor for differentiating between small leaks and variations in soil composition or the presence of roots and other plant matter.
Methods currently exist for detecting and locating leaks from landfills, hazardous waste dumps, impoundments, and other outdoor fluid containment areas by measuring changes in the conductivity and/or resistivity of the adjacent soil. Daily et al. ""406 discloses mise-a-la-masse and electrical resistance tomography leak location methods. Mise-a-la-masse involves driving an electrode within a fluid containment facility to an electrical potential with respect to another electrode placed at a distance from the facility. Voltage differences are then measured between various combinations of additional electrodes placed in the soil adjacent to the facility. The leak location is located by determining the coordinates of a current source pole that best fits the measured potentials within the constraints of the known or assumed resistivity distribution. Because the potentially leaking fluid must be driven to a potential, mise-a-la-masse methods can monitor for leaks in continuous fluid systems only, such as ponds, lined fluid containment areas, and tanks.
Electrical resistivity tomography (ERT) involves placing electrodes around the periphery of, beneath, or, in the case of subsurface containment vessels, above the facility. A known current is applied to alternating pairs of electrodes, then the electrical potential is measured across other alternating pairs of electrodes. From this data the electrical resistivity at a plurality of points in the soil can be calculated. Disturbances in resistivity will correlate with migration of leaking fluid. However, Daily does not disclose a method or apparatus that allows the electrodes to be placed directly under the leak source, after construction of a building or other structure.
Henderson ""202 and ""045 both disclose directly monitoring the soil subjacent to a fluid containment area by burying electrodes directly beneath the containment. Both Henderson patents disclose a plurality of four-plate electrode systems. A voltage and a known current are applied across the outer pair of plates. The resulting potential difference is measured across the inner pair. Henderson ""045 also discloses a system of individual electrodes that, by varying the spacing between the electrodes impressing a current into the ground and the spacing of the potential measurement electrodes, can indirectly measure the resistivity at a calculated depth. However, Henderson ""045 does not disclose a method of directly monitoring the subgrade beneath a structure without permanently burying the electrodes or a method to place electrodes beneath an existing structure.
Woods et. al ""244 discloses a leak detection system for radioactive waste storage tanks. The system comprises a metal tank, an AC generator connected between the tank and a reference electrode, and a plurality of reference electrodes. When the generator is energized, it creates an electric field in the ground between the tank and the reference electrode. A voltmeter measures the potential difference between the sensing electrodes and the tank. A significant change in the potential at one or more of the sensing electrodes indicates that the tank has developed a leak. Woods et al. has a number of disadvantages. First, it requires an electrically conductive fluid container. Second, it requires that the electrodes be permanently buried in the soil surrounding the tank. Finally, it requires the use of an AC generator, which is less convenient than a DC power source.
None of the prior art is entirely satisfactory to locate fluid leaks beneath an existing slab foundation. For instance, it is not practical to electrify the potentially leaking fluidxe2x80x94typically a plumbing systemxe2x80x94and because there may exist multiple sources of fluid, mise-a-la-masse is not a practical option. Nor is it practical to embed permanently a series of electrodes beneath the slab to monitor soil resistivity. Further, because some of the ERT methodsxe2x80x94for example, the Henderson referencesxe2x80x94use multiple-plate electrodes, a large hole would have to be bored into the slab to insert the electrodes into the subjacent soil making the method impractical and destructive. In addition, placing the electrodes around the periphery of the foundation is less accurate compared to placing the electrodes directly beneath the potential leak source. All the prior art electrical mapping methods only map a two-dimensional area, assuming resistivity to be uniform with depth, rather than a three-dimensional volume. Also, all the prior art methods are static. That is, once in place, none of the electrodes are moved to generate different or three dimensional data.
Another potential problem with using existing electrical mapping methods such as ERT to locate leaks beneath a slab foundation is xe2x80x9cnon-uniqueness.xe2x80x9d Non-uniqueness is an ambiguity that arises in data. For instance, a large resistivity anomaly at a large distance from an electrode may generate the same data as a smaller anomaly located close to the electrode. This ambiguity, or non-uniqueness, may mischaracterize the actual subsurface resistivity profile, resulting in a resistivity map that indicates leaks or other resistivity anomalies in incorrect locations.
Accordingly, a need exists for a method for locating fluid leaks and other anomalies beneath slab-on-grade foundations without the need for destroying the slab or permanently burying electrodes beneath the slab. Another need exists for access to the soil beneath the slab as unobtrusively as possible. Further, a need exists for an electrical resistivity mapping method and apparatus for detecting leaks beneath a slab foundation without requiring the electrification of the fluid source. Additionally, a need exists for a method and apparatus to map a three-dimensional subjacent volume""s electrical resistivity with both static and dynamic electrodes. Finally, there is a need for a method and apparatus to minimize or eliminate the errors associated with xe2x80x9cnon-uniqueness.xe2x80x9d
The present invention discloses a method for creating an electrical resistivity model of the volume beneath a subsurface media. The method includes identifying the configuration for placing data collection devices through a media and collecting field data from those data collection devices. An apparent resistivity field is calculated from the collected field data. A standard field model is identified and a regression analysis is performed on the apparent resistivity field and the standard field model. An enhanced field model is prepared from this regression analysis. In a second embodiment, a field model is identified. Next, a geostatistical analysis is selected and performed on the field model creating a new model. Core samples are taken from the media and tested for resistivity. The new model and the results from the testing of the core samples are compared. Because the present invention utilizes soil samples taken from the media, as well as advanced geostatistical mathematical modeling techniques, the present invention allows creation of more accurate resistivity models than those methods disclosed in the prior art. Furthermore, the disclosed electrical resistivity models will allow the user to determine the extent of vegetation and tree root penetration, differences in geology, as well as the existence, extent and location of fluid leaks.
Soil, rocks, and vegetative matter can conduct electricity to varying degrees. The resistance, or resistivity, of these materials to an electrical current will vary depending upon density, particle composition, moisture content, and the chemical composition of fluid in the spaces between the particles. A fluid leak from, for example, pipes in a slab foundation into the subjacent soil will affect the electrical resistivity (electrical resistance offered by a material to the flow of current, times the cross-sectional area of current flow and per length of current path). Liquid leaking from the pipes, through the slab, and into the subjacent soil will soak the soil. Water decreases the resistivity of the subgrade. Measuring soil resistivity at varying depths and at varying locations, both beneath and adjacent to a slab foundation, and comparing these resistivities to one another, allows one the location of soil anomalies based on resistivity variations. These anomalies can include, of course, wet soil, as from a leak. Other anomalies include tree root growth, other vegetative matter, as well as voids or spaces in the soil beneath the foundation. The location of resistivity anomalies will correspond to the location of subgrade soil anomalies.
Resistivity cannot be measured directly; however, resistivity can be computed if the intensity of a current injected into the ground, and the resulting potential difference established between measurement electrodes are measured. These quantities depend on the geometry of the electric field, the nature of the soil and interstitial fluid, and the method used to measure the injected current and the resulting potential difference.
The present invention contemplates converting the measured potential to a resistivity value, assigning the resistivity value to a spatial coordinate, and storing these values in a computer file. A computer program then performs a least squares data inversion analysis on the resistivity and location values, creating a electrical resistivity model that minimizes the error of the field data. Next, another computer program performs a spatial data analysis, or geostatistical analysis, using kriging or other methods. Geostatistics is a branch of applied statistics that focuses on the mathematical description and analysis of geological observations. Kriging is a geostatistical method of evaluating, for example, mine reserves based on a mathematical function known as a semivariogram, or a function used to quantify the dissimilarity between groups of values. This geostatistical analysis produces another electrical resistivity model that minimizes the error of the spatial variability of the measured resistivities. This electrical resistivity model is then analyzed alone or compared to laboratory resistivity measurements performed on soil samples taken from around the structure. This comparison provides a standard or control for the resistivity models so that problems of non-uniqueness are minimized.